Reduction properties of the KP-mKP hierarchy
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929667927179264 |
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| author | Geng, Lumin Hu, Jianxun Wu, Chao-Zhong |
| author_facet | Geng, Lumin Hu, Jianxun Wu, Chao-Zhong |
| contents | The so-called KP-mKP hierarchy, which was introduced recently via pseudo-differential operators with two derivations, can be reduced to the Kadomtsev-Petviashvili (KP), the modified KP (mKP) and the two-component BKP hierarchies. In this note, we continue to study reductions properties of the KP-mKP hierarchy, including its $(n,m)$-reduction and its reduction to a certain extended $r$-reduced KP hierarchy (the $r$-th Gelfand-Dickey together with its wave function). As a byproduct, we show that the Hirota equations of the extended $r$-reduced KP hierarchy follow from those of the mKP hierarchy, which confirms a conjecture of Alexandrov on the open KdV hierarchy in [ J. High Energy Phys. 2015 ]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduction properties of the KP-mKP hierarchy Geng, Lumin Hu, Jianxun Wu, Chao-Zhong Exactly Solvable and Integrable Systems The so-called KP-mKP hierarchy, which was introduced recently via pseudo-differential operators with two derivations, can be reduced to the Kadomtsev-Petviashvili (KP), the modified KP (mKP) and the two-component BKP hierarchies. In this note, we continue to study reductions properties of the KP-mKP hierarchy, including its $(n,m)$-reduction and its reduction to a certain extended $r$-reduced KP hierarchy (the $r$-th Gelfand-Dickey together with its wave function). As a byproduct, we show that the Hirota equations of the extended $r$-reduced KP hierarchy follow from those of the mKP hierarchy, which confirms a conjecture of Alexandrov on the open KdV hierarchy in [ J. High Energy Phys. 2015 ]. |
| title | Reduction properties of the KP-mKP hierarchy |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2501.04984 |